How We Research

A 25 mm eyepiece in a 1200 mm telescope gives 48x. Swap to 10 mm and you get 120x.

Past about 406x, your 8 in tube has nothing more to resolve. We print the formula, then the source.

Two inputs feed every number. A published formula. A maker's spec page, with the date we read it. Pictures carry a credit line.

The path is short. We read the source. We pick the topic, write the formula, and check the maker's spec page.

Before a page goes live, an editor re-runs each cell against the formula and the spec page. A product row is re-read for stock and listing date before it is linked.

Magnification is telescope focal length divided by eyepiece focal length. Tele Vue prints that line. A 2x Barlow takes the 10 mm row from 120x to 240x.

Sky & Telescope states the ceiling two ways. Take 50x per inch of aperture, or 2x per millimeter. On an 8 in tube, 50 times 8 is 400x. Twice 203 mm is 406x.

The calculator prints the millimeter path: 2 times 203 is 406x. Sky & Telescope's inch rule says 400x. The 6x gap is 2x per mm, which is 50.8x per inch.

The low end divides aperture in millimeters by 7. You get the power for a 7 mm exit pupil. For 203 mm the floor is 29x. At 1200 mm, that eyepiece is 41.4 mm.

Exit pupil has two forms, and they have to match. Divide aperture by magnification. Or divide eyepiece focal length by focal ratio. Tele Vue prints both.

For a reflector, flag a pupil under 0.5 mm or over 7 mm. Under 0.5 mm, the view will be dim. Over 7 mm, part of the light misses a 7 mm pupil.

True field is apparent field divided by magnification. A 52° eyepiece at 48x shows 1.08° of sky. Skip the division and you will treat 52° as sky.

If your spec sheet lists a field stop, divide that stop by the telescope focal length, then multiply by 57.3. Tele Vue prints that factor. We use it only when the stop is printed.

Dawes limit is 4.56 arcsec divided by aperture in inches. In millimeters it is 116 divided by aperture. Sky & Telescope prints both. Dawes published the inch form in 1867.

For 8 in, 4.56 / 8 is 0.57 arcsec. And 116 / 203 is 0.57 arcsec. We print 0.57 arcsec.

The calculator's limiting-magnitude line is 2.7 plus 5 times log10 of aperture in millimeters. For 203 mm that is 14.2. Our constants file calls this an average observer on a dark sky.

Light grasp is a different line. Against a 7 mm pupil, 203 mm gathers 841 times the light. That ratio does not set the limiting magnitude.

Maker figures are not formulas. Aperture, focal length, weight, and focuser size come off the maker's spec page. We store the date, because a listing moves.

The worked example follows the Sky-Watcher Flextube 200P. The maker's manual lists that collapsible tube as 200 mm and 1200 mm, and calls it 8 in.

A sky picture comes from a public-domain source we can name, or from a drawing marked as a simulated view. Numbers stay in the diagram and the table. If two sources disagree, both figures stay up.

The magnification calculator divides telescope focal length by eyepiece focal length. The eyepiece calculator turns that power into exit pupil and true field.

The tables share that input set. Aperture. Focal length. Eyepiece focal length. Barlow factor. Apparent field, when your sheet has it. Change one cell and you watch the outputs move.

A table row is the same division the form runs. If JavaScript fails, the formula and the table stay in the HTML.

The calculator enters an 8 in aperture as 203 mm. 8 times 25.4 is 203.2, and we keep 203. Focal length stays at the manual's 1200 mm.

1200 divided by 25 is 48 exactly. 1200 / 203 is 5.91, which we print as f/5.9.

Apparent field is 52° only when the sheet is blank. That is a plain Plössl stand-in. If the maker prints 68° or 82°, you divide by the printed angle.

The gain formula uses a 7 mm pupil, the dark-adapted figure Tele Vue cites. The calculator uses 0.52° for the Moon. NASA lists a mean radius of 1737.4 km and a semimajor axis of 0.3844 million km.

Twice the small angle of radius over distance is 0.52°. A 1.08° field then holds the Moon about 2.1 times.

Dark sky and suburban sky use the Bortle scale John Bortle set in Sky & Telescope, February 2001. The scaled limits sit with the worked numbers below.

You read the 25 mm row first. Power is 48x. Exit pupil is 4.23 mm. True field at 52° is 1.08°. 203 divided by 48 is 4.23 mm.

A 1.25 in 32 mm eyepiece is capped by a 27 mm field stop. 27 / 1200 times 57.3 is 1.29°. Your Moon fits about 2.5 times across. The 6 mm row plus a 2x Barlow is 400x, with a 0.51 mm pupil, still under 406x.

The reference gear in our worked examples is the Sky-Watcher Flextube 200P (S11700). The manual lists 200 mm and 1200 mm. The calculator enters 203 mm and keeps 1200 mm.

The Amazon US listing for S11700, read 2026-10-17, lists 25 mm and 10 mm eyepieces. On 1200 mm those are 48x and 120x. The maker's page only says two 1.25 in eyepieces. The 32 mm, 15 mm, and 6 mm rows are calculator steps.

The Sky-Watcher USA page says 200 mm and 816 times a 7 mm pupil. 200 / 7, squared, is 816. The calculator uses 203 mm, which is 841 times.

These three are generic calculator inputs, not models we name. A 6 in f/8 tube is entered as 150 mm and 1200 mm.

150 times 8 is 1200, so the focal ratio is f/8. The 25 mm eyepiece is still 48x. Exit pupil is 3.13 mm.

The calculator prints 2 times 150, which is 300x. Dawes limit is 0.77 arcsec. The limiting-magnitude line prints 13.6.

A 102 mm f/6.5 refractor needs no focal-length round. 102 times 6.5 is 663 mm. Your 25 mm eyepiece gives about 26.5x and a 3.85 mm pupil. Divide 25 by 6.5 and you get 3.85 mm again.

The calculator prints 2 times 102, which is 204x. The inch rule is about 201x. Dawes limit is 1.14 arcsec. The limiting-magnitude line prints 12.7.

A 127 mm Maksutov at 1500 mm gives 60x with the 25 mm eyepiece. Exit pupil is 2.12 mm. Focal ratio is 11.8. And 25 / 11.8 is 2.12 mm.

The calculator prints 2 times 127, which is 254x. The inch rule is 250x, because 127 mm is 5.00 in. Dawes limit is 0.91 arcsec. The limiting-magnitude line prints 13.2.

Bortle published limits for a 32 cm reflector, not for 203 mm. We scale by 5 log10 of 320 / 203. That shift is 0.99 magnitude. You subtract it, because the smaller aperture reaches a brighter limit.

Class 3 reaches magnitude 16 with the 32 cm reflector, about 15.0 at 203 mm. Class 4 reaches 15.5, about 14.5 at 203 mm. The dark band, class 3 to 4, is about 14.5 to 15.0.

Class 6 reaches 14.0 to 14.5 with the 32 cm reflector, about 13.0 to 13.5 at 203 mm. Class 7 barely reaches 14, about 13.0 at 203 mm. The suburban band is about 13.0 to 13.5.

The calculator prints 14.2. That line is not a Bortle class. The class 3 to 4 band above is about 14.5 to 15.0. Under class 6 you plan on about 13.0 to 13.5.

The box says 675x. That's 900 mm times 3, a 3x Barlow, divided by 4 mm. On a 60 mm lens, 2.4 in, the calculator prints 2 times 60, which is 120x. The inch rule is about 118x.

Flags sit on the form. A 56 mm eyepiece is a 2 in barrel. The Flextube focuser is 2 in, and a 1.25 in eyepiece needs the adapter.

On the 1200 mm tube, 56 mm is 21.4x and the pupil is 9.5 mm, so the low-power flag fires.

A 4 mm eyepiece plus a 2x Barlow is 600x. The pupil is 0.34 mm. The form shows the ceiling flag first, past about 406x. The 0.34 mm pupil is under the 0.5 mm line as well.

Apparent field is not true field. At 48x, 52° becomes 1.08° of sky. The 6 mm plus 2x row is 400x. You do not take 200x times 2 again.

You can rebuild any cell. Divide 1200 by the power you want. At 150x your eyepiece is 8.0 mm, between the 10 mm row at 120x and the 6 mm row at 200x.

If you cannot rebuild a cell from the formula and the source, it stays off the page.